Effective Polynomial Computation:
Effective Polynomial Computation is an introduction to the algorithms of computer algebra. It discusses the basic algorithms for manipulating polynomials including factoring polynomials. These algorithms are discussed from both a theoretical and practical perspective. Those cases where theoretically...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
1993
|
| Schriftenreihe: | The Springer International Series in Engineering and Computer Science
241 |
| Schlagworte: | |
| Online-Zugang: | BTU01 Volltext |
| Zusammenfassung: | Effective Polynomial Computation is an introduction to the algorithms of computer algebra. It discusses the basic algorithms for manipulating polynomials including factoring polynomials. These algorithms are discussed from both a theoretical and practical perspective. Those cases where theoretically optimal algorithms are inappropriate are discussed and the practical alternatives are explained. Effective Polynomial Computation provides much of the mathematical motivation of the algorithms discussed to help the reader appreciate the mathematical mechanisms underlying the algorithms, and so that the algorithms will not appear to be constructed out of whole cloth. Preparatory to the discussion of algorithms for polynomials, the first third of this book discusses related issues in elementary number theory. These results are either used in later algorithms (e.g. the discussion of lattices and Diophantine approximation), or analogs of the number theoretic algorithms are used for polynomial problems (e.g. Euclidean algorithm and p-adic numbers). Among the unique features of Effective Polynomial Computation is the detailed material on greatest common divisor and factoring algorithms for sparse multivariate polynomials. In addition, both deterministic and probabilistic algorithms for irreducibility testing of polynomials are discussed |
| Beschreibung: | 1 Online-Ressource (XI, 363 p) |
| ISBN: | 9781461531883 |
| DOI: | 10.1007/978-1-4615-3188-3 |
Internformat
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| 520 | |a Effective Polynomial Computation is an introduction to the algorithms of computer algebra. It discusses the basic algorithms for manipulating polynomials including factoring polynomials. These algorithms are discussed from both a theoretical and practical perspective. Those cases where theoretically optimal algorithms are inappropriate are discussed and the practical alternatives are explained. Effective Polynomial Computation provides much of the mathematical motivation of the algorithms discussed to help the reader appreciate the mathematical mechanisms underlying the algorithms, and so that the algorithms will not appear to be constructed out of whole cloth. Preparatory to the discussion of algorithms for polynomials, the first third of this book discusses related issues in elementary number theory. These results are either used in later algorithms (e.g. the discussion of lattices and Diophantine approximation), or analogs of the number theoretic algorithms are used for polynomial problems (e.g. Euclidean algorithm and p-adic numbers). Among the unique features of Effective Polynomial Computation is the detailed material on greatest common divisor and factoring algorithms for sparse multivariate polynomials. In addition, both deterministic and probabilistic algorithms for irreducibility testing of polynomials are discussed | ||
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Datensatz im Suchindex
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| dewey-full | 005.131 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 005 - Computer programming, programs, data, security |
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| discipline | Informatik |
| doi_str_mv | 10.1007/978-1-4615-3188-3 |
| format | Electronic eBook |
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| id | DE-604.BV045187167 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:10:59Z |
| institution | BVB |
| isbn | 9781461531883 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030576345 |
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| physical | 1 Online-Ressource (XI, 363 p) |
| psigel | ZDB-2-ENG ZDB-2-ENG_Archiv ZDB-2-ENG ZDB-2-ENG_Archiv |
| publishDate | 1993 |
| publishDateSearch | 1993 |
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| publisher | Springer US |
| record_format | marc |
| series2 | The Springer International Series in Engineering and Computer Science |
| spelling | Zippel, Richard Verfasser aut Effective Polynomial Computation by Richard Zippel Boston, MA Springer US 1993 1 Online-Ressource (XI, 363 p) txt rdacontent c rdamedia cr rdacarrier The Springer International Series in Engineering and Computer Science 241 Effective Polynomial Computation is an introduction to the algorithms of computer algebra. It discusses the basic algorithms for manipulating polynomials including factoring polynomials. These algorithms are discussed from both a theoretical and practical perspective. Those cases where theoretically optimal algorithms are inappropriate are discussed and the practical alternatives are explained. Effective Polynomial Computation provides much of the mathematical motivation of the algorithms discussed to help the reader appreciate the mathematical mechanisms underlying the algorithms, and so that the algorithms will not appear to be constructed out of whole cloth. Preparatory to the discussion of algorithms for polynomials, the first third of this book discusses related issues in elementary number theory. These results are either used in later algorithms (e.g. the discussion of lattices and Diophantine approximation), or analogs of the number theoretic algorithms are used for polynomial problems (e.g. Euclidean algorithm and p-adic numbers). Among the unique features of Effective Polynomial Computation is the detailed material on greatest common divisor and factoring algorithms for sparse multivariate polynomials. In addition, both deterministic and probabilistic algorithms for irreducibility testing of polynomials are discussed Computer Science Symbolic and Algebraic Manipulation Numeric Computing Algebra Number Theory Computer science Numerical analysis Computer science / Mathematics Number theory Polynom (DE-588)4046711-9 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Computeralgebra (DE-588)4010449-7 gnd rswk-swf Polynomalgebra (DE-588)4297306-5 gnd rswk-swf Polynomalgebra (DE-588)4297306-5 s Algorithmus (DE-588)4001183-5 s 1\p DE-604 Polynom (DE-588)4046711-9 s Computeralgebra (DE-588)4010449-7 s 2\p DE-604 Erscheint auch als Druck-Ausgabe 9781461363989 https://doi.org/10.1007/978-1-4615-3188-3 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Zippel, Richard Effective Polynomial Computation Computer Science Symbolic and Algebraic Manipulation Numeric Computing Algebra Number Theory Computer science Numerical analysis Computer science / Mathematics Number theory Polynom (DE-588)4046711-9 gnd Algorithmus (DE-588)4001183-5 gnd Computeralgebra (DE-588)4010449-7 gnd Polynomalgebra (DE-588)4297306-5 gnd |
| subject_GND | (DE-588)4046711-9 (DE-588)4001183-5 (DE-588)4010449-7 (DE-588)4297306-5 |
| title | Effective Polynomial Computation |
| title_auth | Effective Polynomial Computation |
| title_exact_search | Effective Polynomial Computation |
| title_full | Effective Polynomial Computation by Richard Zippel |
| title_fullStr | Effective Polynomial Computation by Richard Zippel |
| title_full_unstemmed | Effective Polynomial Computation by Richard Zippel |
| title_short | Effective Polynomial Computation |
| title_sort | effective polynomial computation |
| topic | Computer Science Symbolic and Algebraic Manipulation Numeric Computing Algebra Number Theory Computer science Numerical analysis Computer science / Mathematics Number theory Polynom (DE-588)4046711-9 gnd Algorithmus (DE-588)4001183-5 gnd Computeralgebra (DE-588)4010449-7 gnd Polynomalgebra (DE-588)4297306-5 gnd |
| topic_facet | Computer Science Symbolic and Algebraic Manipulation Numeric Computing Algebra Number Theory Computer science Numerical analysis Computer science / Mathematics Number theory Polynom Algorithmus Computeralgebra Polynomalgebra |
| url | https://doi.org/10.1007/978-1-4615-3188-3 |
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